Cambridge Additional Mathematics

1

-2 -1 1 2

2

3

4

5

y

x

y= 2 x

A

B

y

x

y=-3

y=2-x-3

2

2

-2 O

-2

All exponential graphs are

similar in shape and have

a horizontal asymptote.

120 Surds, indices, and exponentials (Chapter 4)

We can sketch reasonably accurate graphs of exponential

functions using:

² the horizontal asymptote

² they-intercept

² two other points, for example, when

x=2, x=¡ 2

Example 25 Self Tutor

Sketch the graph of y=2¡x¡ 3.

Hence state the domain and range of f(x)=2¡x¡ 3.

For y=2¡x¡ 3 ,

the horizontal asymptote is y=¡ 3.

When x=0, y=2^0 ¡ 3

=1¡ 3

=¡ 2

) they-intercept is¡ 2.

When x=2, y=2¡^2 ¡ 3

=^14 ¡ 3

=¡ (^234)
When x=¡ 2 , y=2^2 ¡3=1
The domain is fx:x 2 Rg. The range is fy:y>¡ 3 g.
Consider the graph of y=2x alongside. We can
use the graph to estimate:
² the value of 2 xfor a given value ofx, for
example 21 :^8 ¼ 3 : 5 fpoint Ag
² the solutions of the exponential equation
2 x=b, for example if 2 x=5 then
x¼ 2 : 3 fpoint Bg.
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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_04\120CamAdd_04.cdr Tuesday, 14 January 2014 2:39:19 PM GR8GREG